Sports Economics: Present and Future Impact on General Economics: Themenheft 3/Bd. 232 (2012) Jahrbücher für Nationalökonomie und Statistik 9783110511185, 9783828205659

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Sports Economics: Present and Future Impact on General Economics Edited by

Ruud H . Koning and Wolfgang Maennig

Bäker, Contributions Agnes, Tubingen by With

Baumann, Robert, Worcester Massachusetts, USA Dietl, Helmut, Zurich, Switzerland Duschl, Tobias, Zurich, Switzerland Engelhardt, Bryan, Worcester Massachusetts, USA Franck, Egon, Zurich, Switzerland Frick, Bernd, Paderborn Haan, Marco Α., Groningen, The Netherlands Haas, Hartmut, Cologne Kamst, Richard, Groningen, The Netherlands Koning, Ruud H., Groningen, The Netherlands Kuper, Gerard H., Groningen, The Netherlands Lang, Markus, Zurich, Switzerland

Lucius &c Lucius · Stuttgart 2 0 1 2

Leeds, Eva Marikova, Bethlehem, USA Leeds, Michael Α., Philadelphia, USA Matheson, Victor Α., Worcester Massachusetts, USA Mechtel, Mario, Trier and Tübingen Niiesch, Stephan, Zurich, Switzerland Ruud Η. Koning, Groningen, The Netherlands Sierksma, Gerard, Groningen, The Netherlands Siissmuth, Bernd, Leipzig Talsma, Bertus G., Groningen, The Netherlands Theiler, Philipp, Zurich, Switzerland van Witteloostuijn, Arjen, Antwerpen, Belgium Vetter, Karin, Tübingen Wagner, Stefan, Berlin Wallbrecht, Björn, Paderborn

Guest Editors Professor Dr. Ruud H. Koning Dept. Economics Econometrics & Finance University of Groningen PO Box 8 0 0 9 7 0 0 AV Groningen The Netherlands r. [email protected] Professor Dr. Wolfgang Maennig University of Hamburg Department of Economics Chair for Economic Policy Von-Melle-Park 5 2 0 1 4 6 Hamburg [email protected]

Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.d-nb.de abrufbar ISBN 9 7 8 - 3 - 8 2 8 2 - 0 5 6 5 - 9

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Satz: Mitterweger Sc Partner Kommunikationsgesellschaft mbH, Plankstadt Druck und Bindung: Neumann Druck, Heidelberg Printed in Germany

Jahrbücher f. Nationalökonomie u. Statistik (Lucius & Lucius, Stuttgart 2012) Bd. (Vol.) 232/3

Inhalt / Contents Guest Editorial

204-209

Abhandlungen / Original Papers Franck, Egon, Philipp Theiler, One for Sure or Maybe Three. Empirical Evidence for Overtime Play from a Comparison of Swiss Ice Hockey and the N H L Bäker, Agnes, Mario Mechtel, Karin Vetter, Beating thy Neighbor: Derby Effects in German Professional Soccer Nüescb, Stephan, Hartmut Haas, Empirical Evidence on the „Never Change a Winning Team" Heuristic Siissmuth, Bernd, Stefan Wagner, A Market's Reward Scheme, Media Attention, and the Transitory Success of Managerial Change Leeds, Eva Marikova, Michael A. Leeds, Gold, Silver, and Bronze: Determining National Success in Men's and Women's Summer Olympic Events Kamst, Richard, Gerard H. Kuper, Gerard Sierksma, Bertus G. Talsma, InnerOuter Lane Advantage in Olympic 1000 Meter Speed Skating Baumann, Robert, Bryan Engelhardt, Victor A. Matheson, Employment Effects of the 2002 Winter Olympics in Salt Lake City, Utah Haan, Marco Α., Ruud H. Koning, Arjen van Witteloostuijn, The Effects of Institutional Change in European Soccer Dietl, Helmut, Tobias Duschl, Egon Franck, Markus Lang, A Contest Model of a Professional Sports League with Two-Sided Markets Frick, Bernd, Björn Wallbrecht, Infant Mortality of Professional Sports Clubs: An Organizational Ecology Perspective

210-223 224-246 247-257 258-278 279-292 293-307 308-317 318-335 336-359 360-389

Buchbesprechung/Book Review Gilli, Manfred, Dietmar Maringer, Enrico Schumann, Numerical Methods and Optimization in Finance

390

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Guest Editorial Sport is of increasing interest and the academic field of sports economics is attracting escalating attention. Figure 1 compares Google hits for "sport", "art", "work", "peace" and "love" since 2004 (starting year of the google search data base) and indicates the relative (and absolute) increasing importance of sports in our daily life. Figure 2 serves as an indicator of the increasing impact and acceptance of sports economics. The number of "sport"-related publications the Web of Science-categories "Economics", "Business", "Business Finance" and "Management" in the twenty years between 1991 and 2011 increased by the factor 29.9, while publications related to "Business Cycle" and "Monetary Policy" increased by the factors 7.3 and 6.3. The absolute number of "sport"-publications in these categories (209) equals to an astonishing 25 % of the "monetary policy"-publications in these categories (838). The increasing importance of sports economics in academic research might be related to the growing importance of sport in daily life; researchers are starting to use sport as a test bed and sports policies as natural experiments to deliver insights into human behaviour that could well be relevant for general labour markets, industrial economics and regional economics. There are no indications that the quantitatively and qualitatively increasing impact of sports economics will end soon. With the growing number of publications, the field of sports economics is becoming both more diverse and less transparent. This special issue provides a snapshot of the current state of the field of sports economics. Most of the contributions provide perspectives for further research. However, we use the opportunity provided by this special issue to identify general trends in sports economics and to summarise potential future developments.

Sport as an ideal field test of human economic behaviour Economics is about human behaviour, and the economic crises of recent years have led to widespread doubt about whether economic concepts are still relevant in explaining the decisions of principals and agents. In particular, the cornerstone of economics, the homo oeconomicus model, is under attack. In their contribution on overtime play in Swiss ice hockey, Franck and Theiler summarise typical theoretical economic reasons for the effects of rule changes in US and Swiss ice hockey. An increase in the incentive to win a game in regular time actually leads to a greater number of games being decided in regular time. The authors present a first empirical test of these traditional considerations and find support for this theoretical prediction, indicating that economic theory is not wrong in all instances. There is evidence that the assumption of rational behaviour may be violated because of differences between perceived and real parameter values and because of information asymmetries. Sports economics may add to this. Soccer players, who now have access to a regime of well-balanced monetary incentives, are believed to be less susceptible to emotional or irrational actions in the setting of a soccer game: we assume that they will always give their best to try to win the match. Bäker, Mechtel and Vetter elaborate on derby effects in German professional soccer; they find that such emotionally charged games are not significantly different from regular games. Derbies tend to be important for spectators and fans, but the authors provide evidence that the players are not affected by the special status of such games.

Guest Editorial · 205

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In a similar vein, Niiesch and H a a s challenge the rational economics view that decisionm a k e r s c a n n o t extract extra profits f r o m analysis of ex post data; exclusively, (superior) expectations o n f u t u r e developments can do. They elaborate on w h y coaches d o not change winning teams. If teams d o not change, coaches do. Siissmuth and Wagner study the relations between public attention, incentives a n d the success of managerial change. Sport again provides an interesting test case in which r e w a r d s , incentives, a n d factors such as media attention substantially vary, allowing economists to identify the effect of managerial change. Emotions, long neglected in the rational analysis of economics, m a y find a role in m o d e r n economics, especially based on insights f r o m sports economics, both as a dependent variable of physical activity and sport c o n s u m p t i o n , for example, or as an antecedent t h a t determines decision processes (Kang et al. 2011). M o r e generally, economic research, in its struggle to find additional violations of the model of h o m o oeconomicus, has preferably used laboratory experiments, which might suffer f r o m systematic bias. Sport does not involve the p r o b l e m of reality tests, a n d is an ideal field test for h u m a n economic behaviour. We trust that the economics literature will m a k e even more use of this o p p o r t u n i t y in the future.

Gender, diversity, fairness and equality Gender, diversity, fairness and equality might well play a greater role in economics in the future; the concept of increasing gaps between small a n d large a n d rich a n d poor, as well as an awareness of discrimination, evolved before the current economic crisis. Again,

2 0 6 · Guest Editorial

Publications listed in Web of Science-categories "Economics", "Business", "Business Finance", "Management" for search items.... 900

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sport (economics) might contribute even more significantly to this discussion than it has done up to now. Modern sport is based on fairness and equality, so it is astonishing that the rules, incentives and economic problems of sports regulation and governance as a showcase for politics, business and other areas have not been studied with greater intensity. The contribution of Leeds and Leeds on female medal winners is relevant in such a discussion because they demonstrate how the political and economic settings of a nation influence the potential of women to develop their abilities and talents. Their contribution implicitly explains other findings that confirm that the gender gap has narrowed over the last decades, findings that are not compatible with the hypothesis that gender differences in competitiveness reflect evolved biological differences and/or psychological predispositions (Frick 2 0 1 1 ) . Translation to a debate not limited to sports is easy: the policies of certain nations prevent full development of the productivity of at least half, if not much more, of the population. While some decision- makers might not care about welfare losses for individual women, they might be more open to a debate about national wealth. In their contribution on 1 0 0 0 m speed skating, Kamst, Kuper, Sierksma and Talsma discover systematic bias. Rules that managed competition satisfactorily and met fairness standards for years may not provide a level playing field today. Their analysis might provide a means to examine more closely (economic) activities, rules and regulations that seem to be fair to the broad majority, but may not be able to cope with current advances in technology and performance. The impact of sports economics in the field of ethics is by no means limited to such discussions. Take, for example, the fight against corruption: impressive policy changes in amateur boxing and ice skating, their acceptance by spectators and competitors (Ko et al. 2 0 1 1 ) and their impact on corruption and on the sport itself are worth studying as a showcase for international business and politics. Other examples include the debate on relationships among sexual orientation, diversity and performance (Cunnigham 2 0 1 1 ) and on the benefits (and costs) of diversity programs in sports (Myers 2 0 1 1 ) and new evidence on salary discrimination in sport (Holmes 2 0 1 1 ) .

Guest Editorial · 207

Sport mega events, economic impact and happiness: a new or re-opened debate? Baumann, Engelhardt and Matheson show that the 2002 Winter Olympics in Salt Lake City increased leisure-related industries in the short run and potentially in the long run. However, the results indicate that the Games had no long-term impact on trade or total employment. Some of these authors belong to the group of scholars who some 20 years ago started a revolution by systematically questioning the view that (mega) sport events generate a positive economic impact. Indeed, their revolution seemed to have arrived at a broad consensus, at least among academics: there are hardly any significant effects on hard-core economic variables such as income, employment and taxes. To the surprise of many, a counter-revolution may have started in the recent past. Rose and Spiegel (2011) find that countries that host the Olympic Games experience significant positive and lasting effects on exports of more than 20 Brückner and Pappa (2011) find that hosting of the Olympic Games induces permanent increases in investment, consumption and output, even before the Games are hosted. They also find - at least at a transitory level - anticipation effects in countries that bid for the Games. The simulation of the 2000 Olympic Games in Sydney by Giesecke and Madden (2011) indicates that economic activity in New South Wales was 0.3 % higher because of the Games over the 12-year period examined. Tien et al. (2011) confirm short-term effects on gross domestic product performance and unemployment, and Fourie and SantanaGallego (2011) find positive impacts on tourism. In addition, authors such as Matheson et al. are ready to search for other rationales to explain why nations or cities should apply for mega events. One of the most prominent arguments is about happiness, and there is some empirical evidence of such effects. Future insights from sports economics will inseminate the research area of happiness. Up to now, sports economics has revealed that sport may influence happiness directly and indirectly via its effects on access to better jobs and on obesity.2 Evidence from sports events might open an avenue for broader analysis of the role and value of cultural and image benefits, local pride and integration in happiness (Balduck et al. 2011; Huang/Gao 2011). Otherwise, the perceived success of a sports event tends to be determined by the enthusiasm of the local community, which could be used to identify strategies for maximizing the net impact of sports events. The so-called boost effect contrasts with findings that American salary earners reduce their working hours during a soccer World Cup by 9-28 minutes per week when the timing of live broadcasts in the USA overlaps with their normal working hours (Lozano 2011), indicating that production losses can be attributed to sports. The debate on the economic effects of mega sport events seems to be open again, and the results, as well as the tools, methods and data used in this debate, will be important in a more general discussion on regional development and competitiveness. In any case, almost all studies on the economic importance of sport reach the conclusion that it accounts for some 1.5-3 % of GDP, and there does not seem to be a trend for an increase in this proportion (Milano/Chelladurai 2011).

Competition policy and industrial economics Sport as an industry has been an important area for application of models of competition policy and industrial economics. In fact, one of the first papers in sports economics dis1 2

For a critical assessment, see Maennig and Richter (2012). See the contributions in Rodriguez (2011).

208 · Guest Editorial

cussed potential distortions of the labour m a r k e t due to the transfer system for baseball players in the USA (Rottenberg 1956). Since then, labour m a r k e t issues and competitive balance have been i m p o r t a n t areas of research. W i t h state f u n d s f r o m China and other nations being invested in European a n d US industries, insights into h o w wealthy investors m a y change competition in professional team sports (Lang et al. 2011) m a y help in f o r m u l a t i n g economic policy. H a a n , Koning and Van Witteloostuijn analyse t w o m a j o r developments in the European soccer market: the development of an open labour market in the EU and the emergence of the Champions League as an important supranational league. Using a theoretical model, they assess h o w these institutional changes affect competitive balance in national competitions and the distribution of international quality differences. The predictions of this model provide insights into current developments in European soccer and are relevant to other sports as well. A different angle is t a k e n by Died, Duschl, Franck and Lang in this volume. Teams compete both as e n t e r t a i n m e n t a n d as a p l a t f o r m for sponsors and fans. T h e authors focus on the n e t w o r k effects provided by sport leagues. T h e resulting n e t w o r k externalities m a y affect competitive balance in a sports league, the very p r o d u c t t h a t is offered to the f a n . T h e existence of some degree of competitive balance has been i m p o r t a n t in regulatory decisions o n the special status of sport. Frick and Wallbrecht s h o w in their contribution t h a t entry and exit in t o p sports leagues take a special f o r m t h r o u g h p r o m o t i o n a n d relegation. " H o w long is a team able to perf o r m at the highest level?" is an i m p o r t a n t question considering the (usually public) investment in stadiums a n d infrastructure necessary to play at t h a t level. N e w m a r k e t s a n d new d e m a n d should result in new research questions relevant for antitrust regulators. Leagues will remain monopolist with the usual targets in price setting, but there is widespread sentiment t h a t at least the most i m p o r t a n t sports events should be s h o w n on "free T V " . N e w technology (e. g. for televisions) has increased the m a r k e t size for any team and supranational leagues such as the C h a m p i o n s League have increased in economic a n d sporting significance. Sport is a p l a t f o r m that allows sponsors to meet each other and fans, and is frequently w a t c h e d on television. Traditional d e m a n d and welfare analyses based on spectator d e m a n d at games in national leagues are n o w of m o r e limited interest. Conclusion T h e r e are plenty of indications that sports economics m a y still increase in i m p o r t a n c e . It already has a superior - at least in p a r t - data basis. Collection of more and better data m a y well enhance the economic database even more. Sports economics to date has focused on developed nations; extension to developing nations should lead to f u r t h e r insights into developing economies. In the current economic climate, a note on financing is in order. Sport, with its differences in financing schemes across nations, time periods, sports disciplines and even gender, provides a n a t u r a l source of experiments t o exploit and to help in understanding economic structures in other areas as well. The papers in this volume provide a m o d e r n overview of important topics in sports economics. A variety of themes are discussed and directions for current and future research are identified. It will be fascinating to see h o w this field develops during the next 10 years.

Guest Editorial · 209

We hope that this volume will bring the opportunities and challenges of sport and sports economics to a broader public. We thank the editors of the Journal of Economics and Statistics for the opportunity to compile this volume.

References Balduck, A.-L., M. Maes, M. Buelens (2011), The social impact of the Tour de France: comparison of residents' pre- and post-event perceptions. European Sport Management Quarterly 11 91-113. Brückner, M., E. Pappa (2011), For an Olive Wreatch? Olympic Games and Anticipation Effects in Macroeconomics. CEPR Discussion Paper 8516, www.cepr.org/pubs/dps/DP8516.asp Cunningham, G. B. (2011), The LGBT advantage: examining the relationship among sexual orientation diversity, diversity strategy, and performance. Sport Management Review 14: 453-461. Fourie, J., M. Santana-Gallego (2011), The impact of mega-sport events on tourist arrivals. Tourism Management 32: 1364-1370. Frick, B. (2011), Gender differences in competitiveness: Empirical evidence from professional distance running. Labour Economics 18: 389-398. Giesecke, J. A. D., J. R. Madden (2011), Modelling the economic impacts of the Sydney Olympics in retrospect: game over for the Bonanza story? Economic Papers 30(2): 218-232. Holmes, P. (2011), New evidence of salary discrimination in major league baseball. Labour Economics 18: 320-331. Huang, H., H. Gao (2011), Estimation of the Non-market Value Generated by 2 0 0 9 Shanghai ATP Masters 1000: A Case Study of the Value of Civic Pride. Pp. 549-554 in: Q. Zhou (ed.), Advances in Applied Economics, Business and Development. Heidelberg: Springer. Kang, J.-H., R. P. Bagozzi, J. Oh (2011), Emotions as Antecedents of Participant Sport Consumption Decisions: A Model Integrating Emotive, Self-Based, and Utilitarian Evaluations. Journal of Sport Management 7: 314-325. Ko, Y. J., Κ. Cattani, Y. Chang, Y. Hur (2011), Do spectators and competitors accept the use of scoring technology in Teakwondo competitions? International Journal of Sport Management and Marketing 9: 238-253. Lang, M., M. Grossman, P. Theiler (2011), The sugar daddy game: how wealthy investors change competition in professional team sports. Journal of Institutional and Theoretical Economics 167: 557-577. Lozano, F. A. (2011), The flexibility of the workweek in the United States: Evidence from the FIFA World Cup. Economic Inquiry 49: 512-529. Maennig, W., F. Richter (2012), Exports and Olympic Games: Is there a Signal Effect? Hamburg Contemporary Economic Discussions No. 42. Milano, M., P. Chelladurai (2011), Gross Domestic Sport Product: The Size of the Sport Industry in the United States. Journal of Sport Management 25: 24-35. Myers, S. L. (2011), The economics of diversity : the efficiency vs. equity trade-off. Pp. 47-61 in: S. Chen (ed.), Diversity management: Theoretical Perspectives and Practical Approaches. Nova Publishers. Rodriguez, P. (ed.) (2011), The economics of sport, health and happiness. Cheltenham etc.: Elgar. Rose, A.K., M . M . Spiegel (2011), The Olympic Effect. The Economic Journal 121: 652-677. Rottenberg, S. (1956), The Baseball Players' Labor Market. Journal of Political Economy 64: 242-258. Tien, C., H. Lo, H. Lin (2011), The economic benefits of mega events: a myth or reality? A logitudinal study of Olympic Games. Journal of Sport Management 25: 11-23. Ruud H. Wolfgang

Körting Maennig

Jahrbücher f. Nationalökonomie u. Statistik (Lucius & Lucius, Stuttgart 2012) Bd. (Vol.) 232/3

One for Sure or Maybe Three Empirical Evidence for Overtime Play from a Comparison of Swiss Ice Hockey and the NHL By Egon Franck and Philipp Theiler, Zurich* JEL D23; L83 NHL; Swiss Ice Hockey National League; overtime; incentive effects; three-point rule; rule-changes.

Summary In order to avoid too many tied games after playing the five-minute overtime period, the National Hockey League (NHL) introduced two rule changes in the 1999-2000 season. First, a team that loses in overtime receives one point instead of zero points. Second, the number of skaters in overtime is reduced from five to four. The theoretical literature analyzing these rule changes predicted that they would also produce the unintended side-effect that more games would reach overtime and recommended that a team that wins in regulation should receive three points (instead of two) in order to counterbalance the converse effect. We are the first to empirically support this theoretical prediction using N H L data and data from Swiss ice hockey, in which the rule changes of the N H L were copied in the 2006-2007 season and in which the three-point rule was also introduced.

1

Introduction

In the National Hockey League ( N H L ) , North America's top professional hockey league, league officials came to the conclusion during the 1990s that too many games were ending in a tie after overtime. 1 Based on the assumption that sports fans like to see a winner after devoting two or three hours to watching a game, the N H L decided to change the rules prior to the 1999-2000 season in order to maintain and increase the demand for its product. Starting with the 1 9 9 9 - 2 0 0 0 season, a team that loses in overtime receives one point instead of zero points. It was conjectured that the old rule rewarded defensive play in overtime. Instead of playing offensively and risking a loss (zero points), teams would prefer to play defensively and secure a tie (one point). By treating ties and overtime losses symmetrically, the new rule was expected to increase the incentives for offensive play in overtime. Moreover, the number of skaters in overtime was reduced from five to four (plus the goal keeper). Removing a skater was likewise expected to promote offense, * We are grateful to J a s o n Abrevaya, Leif Brandes, two anonymous referees, and seminar participants at the University of Zurich for helpful comments. Special thanks go to Christian Wassmer and Martin Merk for providing us with the data. Sabrina Biittler provided excellent research assistance. All remaining errors are our own. This article is based on the second author's dissertation. Department of Business Administration, University of Zurich, Switzerland. 1 See Abrevaya (2004: 293).

One for Sure or Maybe Three · 211

since four-on-four play increases the speed of the game, making defensive strategies more difficult to implement. As a result, the rule changes yielded the intended effect, when the percentage of overtime games ending in a tie fell. However, the rule changes also had a measurable converse effect 2 : The percentage of games reaching overtime rose. In order to mitigate this converse effect, alternatives to the rule changes implemented in the N H L have been proposed in the literature: Awarding three points for a win in the regulation time, the use of fouron-four play for a longer overtime period (e.g., from now 5 minutes to 10 minutes), and the introduction of a shootout after an undecided overtime have all been suggested. Most attention was given to the introduction of the three-point rule. Abrevaya (2004), Longley and Sankaran ( 2 0 0 7 ) , and Banerjee et al. (2007) all remark that awarding three points to the winner of a game after the 6 0 minutes of the regulation time would reduce the portion of games reaching overtime. Whereas Abrevaya's study solely suggests the three-point rule as a possible alternative, the latter two studies support their conclusions with their respective theoretical models. At the simplest level, the intuition leading to fewer overtime games through the introduction of the three-point rule can be stated as follows: By awarding three points to the winner for a game decided in the regulation time, the rule change simply increases the total available payoff from two to three points. The larger 'pie' transforms a win in the regulation time into a more desirable outcome. 3 No empirical evidence is available at the time, since the N H L did not introduce the threepoint rule. However, the Swiss Ice Hockey National League (Swiss NL) went through a major rule change prior to the 2 0 0 6 - 2 0 0 7 season, which included the introduction of the three-point rule. Compared to the rules that the N H L introduced in the 1 9 9 9 - 2 0 0 0 and 2 0 0 5 - 2 0 0 6 seasons, the rules that the Swiss N L introduced in the 2 0 0 6 - 2 0 0 7 season are different only in terms of the three-point rule. It follows that, by defining adequately observed pre-change periods and post-change periods for the N H L and the Swiss NL, the only remaining difference concerning the point-awarding system between the two can be reduced to the three-point rule. Although supportive theoretical models are presented in the literature, the question whether the three-point rule really mitigates the converse effect finally remains an empirical one. We are able to provide the first empirical support for the theoretical predictions made in the literature concerning the effect of the three-point rule. It seems that the three-point rule contributes to damp the converse effect that more games reach overtime. Matched data from both leagues' regular seasons allow us to empirically compare and examine the two incentive schemes and to draw our conclusions. One point requires more consideration: the objective function of the league. Abrevaya (2004) discusses the objective functions of the different agents and states that more games reaching the overtime do not have to be a bad state for the league. In this sense, we do not know whether the indicated converse effect is really unintended from the perspective of the N H L . Independent of whether the effect was intended, the focus of this work lies in the analysis of the reasons for the behavior of the teams after the rule changes

2

3

Abrevaya ( 2 0 0 4 ) calls this effect 'unintended', Banerjee et al. ( 2 0 0 7 ) call it 'perverse'. Although these normative conjectures might be true, we do not know precisely which goals the league intended t o reach with the rule changes. We call the effect 'converse'. See Abrevaya ( 2 0 0 4 : 2 9 6 ) .

2 1 2 · Egon Franck and Philipp Theiler

in the respective leagues a n d whether the theoretical predictions a b o u t this behavior were correct or not. T h e paper is organized as follows. In the next section, w e briefly review related studies. Thereafter, the rule changes in the N H L a n d the Swiss N L with their basic incentive effects are briefly explained. We then t u r n to the d a t a c o m p a r i s o n by presenting some descriptive findings of the different leagues, which we then supplement with the results of a p r o b i t regression analysis controlling for other factors that might influence the occurrence of an overtime. T h e final section concludes and reflects on the potential limitations of our a p p r o a c h .

2

Literature

Abrevaya (2004) was the first to study the incentive effects of the rule changes in the N H L in 1999. 4 H e analyzed these effects by identifying different scenarios and payoff distributions a n d applying decision theory. As a result, he showed that the rule changes yielded the intended effect, since the percentage of overtime games ending in a tie fell. However, the rule changes also had a converse effect: T h e percentage of overtime games rose. Longley a n d S a n k a r a n (2007) proposed a general f o r m a l model of strategic behavior for the N H L . They added the insight that the decision to a d o p t a n offensive or a defensive on-ice strategy crucially depends o n a team's perception of its o w n strengths relative to those of its o p p o n e n t . Their model shows that not all teams find it beneficial to a d o p t a defensive playing style during the regulation time after the rule change. However, they agree t h a t more games reach overtime after the rule change, based on their theoretical model. Banerjee et al. (2007) developed a game-theoretic model that determines optimal team strategies under alternative overtime p o i n t - a w a r d i n g systems for the N H L . All three publications finally c o m e to the conclusion that a w a r d i n g three points to a winner in the regulation time could mitigate the above mentioned converse effect. However, none of these w o r k s present empirical evidence t o s u p p o r t the theoretical conclusions. A n u m b e r of studies have looked at the introduction of the three-point rule in football. For example, Guedes a n d M a c h a d o (2002) analyze the influence of the three-point rule on the attractiveness of the Portuguese first football division. While they d o not find evidence that the three-point rule impacted on the p r o p o r t i o n of tied games, they s u p p o r t the more general prediction of Longley and S a n k a r a n (2007) that not all teams will a d o p t the same strategy after rule introduction. Inquiring into the G e r m a n situation Dilger a n d Geyer (2009) deliver empirical evidence t h a t the fraction of games ending in a tie significantly decreased after the introduction of the three-point rule in Germany. After developing a theoretical model predicting that the p r o p o r t i o n of tied games should decline with the introduction of a three-point rule in football, Moschini (2010) finds empirical s u p p o r t for this prediction based on d a t a f r o m 35 countries. Although most of the empirical results f r o m football are in line with the expectation that the introduction of the three-point rule should reduce the n u m b e r of tied games, the relevance of these findings is rather limited for the topic of our study. T h e reason is quite obvious: there is n o post-regular time stage like an overtime in football! 4

Section 3 explains the relevant changed elements in the N H L in more detail.

One for Sure or Maybe Three · 213

3

The leagues and their changes

The N H L is North America's major professional ice hockey league. It is divided into two conferences, each with three divisions. Each division consists of five teams. The points gained during the regular season determine the standings of the teams. The best eight teams of each conference according to the respective standings enter the post-season (the playoffs) and compete with each other to win the Stanley Cup. Our sample period for the N H L consists of the regular seasons 1997-1998, 1998-1999 and 2 0 0 5 - 2 0 0 6 to 2008-2009.5 The Swiss Ice Hockey National League (Swiss N L ) is the major (semi-)professional ice hockey league in Switzerland. It is divided into National League A (NLA) and National League Β (NLB). There are no conferences within the N L A or the N L B . Whereas the N L A is the top division of the Swiss N L , the N L B is the minor division, where most players are semi-professionals. Clubs are allocated between the two divisions at the end of every season based on sportive merit. Though these divisions are linked through promotion and relegation at the end of every season, their teams play a completely independent regular season and playoffs. As in the N H L , the points gained during the regular season determine the division standings of the teams, and the best eight teams according to the division standings enter their respective playoffs at the end of the regular season. The division standings dictate the seeding of teams in the playoffs. Teams compete directly with each other in their division for a slot in the playoffs. Therefore, every game has the same ex-ante importance for reaching the playoffs. We have match data from the 2 0 0 1 - 2 0 0 2 through 2 0 0 8 - 2 0 0 9 regular seasons for the N L A and the N L B . In both leagues, the N H L and the Swiss N L , a regular season game lasts 60 minutes, divided into three periods of 2 0 minutes. A five-minute overtime period is played if regulation time ends in a tie. The four rule changes addressed in this paper are as follows 6 : Element 1: The winner in the regulation time receives three points (instead of two). Element 2: The winner in overtime receives two points, but the loser receives one point (instead of zero). Element 3: The winner in the shootout, which now follows a tied five-minute overtime period, receives two points and the loser one point. Element 4: The number of skaters in overtime is reduced from five to four (plus the goal keeper). Elements 2 and 4 were introduced by the N H L prior to the 1999-2000 season. Element 3 was introduced by the N H L prior to the 2 0 0 5 - 2 0 0 6 season. Elements 1, 2, 3, and 4 were introduced by the Swiss N L prior to the 2 0 0 6 - 2 0 0 7 season. Figure 1 depicts the exact introduction time-line of the rule changes in the N H L and the Swiss N L .

5

6

The N H L seasons from 1 9 9 9 - 2 0 0 0 to 2 0 0 3 - 2 0 0 4 are not relevant, because during this period the shootout rule was not implemented (see Figure 1 and explanation below). Additionally, a lock-out 'spoiled' the 2 0 0 4 - 2 0 0 5 season. Some other rule modifications were made in both leagues together with the mentioned major changes. Prominent examples are tightened rules concerning clutching-and-grabbing interference and smaller goaltender equipment size. Additionally, the two-line pass was legalized in the N H L , as it already was the case a longer time a g o in the Swiss N L .

214 · Egon Franck and Philipp Theiler

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Figure 1 Rule changes over time in the NHL and the Swiss NL Table 1 sums up the different point-awarding systems resulting from the rule changes in the N H L and the Swiss NL. It is important to notice that both organizations had the same point-awarding system before their respective rule changes (1999 in the N H L and 2006 in the Swiss NL). After all of these changes (since 2005 in the N H L and since 2006 in the Swiss NL), both organizations again have the same point-awarding system with one exception: in the Swiss NL, the winner in the regulation time is awarded three points instead of two. The incentive effect of element 1, the three-point rule, is linked to the increase of the total payoff for a game decided in the regulation time from two to three points. As a result, the potential 'pie' available for the two teams in regulation time and in overtime is identical. However, in regulation time, this entire 'pie' will be awarded to the winner. In terms of net points (relative to the opponent), a win in regulation time gives the winner three points to make a difference to his opponent. A win in overtime or after the shootout Table 1 Point awarding system in the NHL and in the Swiss NL

Points awarded for Win in Defeat Win in Defeat Tie Win in Defeat

regulation time in regulation time overtime in overtime the shootout in the shootout

Old Rules NHL (until 1998) & Swiss NL (until 2005) 2 0 2 0 1 -

New Rules NHL Swiss NL (since 2005) (since 2006) 2 0 2 1

3 0 2 1

-

-

2 1

2 1

One for Sure or Maybe Three • 215

only makes a net difference of one point between the winner and the loser. While element 2, the overtime-loss rule, makes losing in overtime more attractive than losing in regulation time, element 1 makes winning in regulation time more desirable than winning in overtime. According to Longley and Sankaran (2007), it is not beneficial for all teams to adopt an offensive strategy. The choice of the strategy depends on the team's own perception of its playing strength relative to the opponent. Teams perceiving themselves as weak may try to play defensively in order to reach overtime and obtain one 'secure' point. However, as the authors show, even with only two points awarded to the winner during regulation time, teams perceiving themselves as strong may have incentives to play an offensive style in overtime. These incentives to play offensively in regulation time may become even more pronounced with the introduction of the three-point rule. Whereas element 2 tends to encourage defensive strategies in regulation time for teams perceiving themselves as weak in order to avoid the zero-point payoff, element 1 sets incentives for an even more offensive playing style for teams perceiving themselves as strong. Element 2, called the overtime-loss rule, was changed because it was conjectured that the old rule rewarded defensive play in overtime. Instead of playing offensively and risking a loss (zero points), teams would prefer to play defensively and secure a tie (one point). 7 With the introduction of element 3 ties are no longer possible. One team has to win, and the realized point difference will now be one point only, regardless of whether the decision is reached during overtime or through a shootout. This smaller point difference together with the absence of a possible tie is expected to increase the incentives for offensive play in overtime. Removing a skater during the overtime (element 4) is expected to produce a similar effect, since four-on-four play increases the speed of the game, making defensive strategies more difficult to implement. 8 The introduction of element 3, the shootout, simply excludes the possibility of two teams earning one point each. It is clear that one team will win and improve its relative position compared to its opponent in the standings after the shootout. On the one hand, the teams perceiving themselves as strong should try harder to win the game during overtime as the shootout decision could be more stochastic. On the other hand, teams perceiving themselves as weak compared to the actual opponent during overtime could try to reach the shootout because their chance of winning could be higher in the more stochastic setting than in normal play during the overtime. 9 This inclination could even be enhanced by the perception that the weaker team has a high-performing shootout goal keeper or excellent shooters. These incentives induced by element 3 may be effective during the regulation time as well. Strong perceiving teams may reduce the likelihood of an overtime and the possible 'lucky' shootout and try harder to play an offensive style in order to win in the regulation time. Weak perceiving teams instead may already start playing defensively during the 7 8

9

See Abrevaya (2004: 295). In the N H L and the Swiss NL, both elements were introduced simultaneously. Abrevaya (2004: 298), examined the effects of the separate introduction of element 2 and 4 in the American Hockey League (AHL). H e figured out that the introduction of the overtime-loss rule as the only changed element increased the number of games going into overtime in that league. Match data from the N H L combined with the match betting odds s h o w that the probability that the ex-ante better team wins the shootout is lower than a win during the five minute overtime period. Albeit this difference is not big, it is an indication that the incentive effects might be effective for the teams.

216 · Egon Franck and Philipp Theiler

regulation time, hoping for the assured point in the overtime and a possible win in the overtime or shootout where they may perceive to have more chances to win. The considerations from above give reason to conclude that the introduction of all four elements together have the incentive effects the literature predicts: M o r e games will be decided during the five-minute overtime period while the portion of games reaching overtime will stay stable.

4

After the changes

The rule changes in the N H L caused the effect that the percentage of overtime games ending in a tie 10 fell from 7 3 . 9 8 % in the pre-change period (1997-1998 to 19981999) to 55.91 % in the post-change period (2005-2006 to 2008-2009). 1 1 However, the rule changes also had the discussed converse effect. Namely, the percentage of games reaching overtime rose from 20.34 % to 22.68 % after the rule changes. 1 2 After the rule changes, the percentage of games reaching overtime and ending in a tie after overtime dropped from 15.05 % to 12.68 % . This decrease would be higher if not counter-balanced by the described converse effect. The first rows in Table 2 summarize the mentioned numbers for the N H L . Despite the fact that we differ in the observation periods, these numbers are similar to those provided by Abrevaya (2004). One could argue that the statistic 'percentage of O T games ending in a tie' from Table 2 is superfluous to indicate after the introduction of the shootout as there is always a winner now. In the pre-shootout era, the statistic 'percentage of O T games ending in a tie' was meaningful, because it showed the league the extent to which it was still not getting its preferred result - i. e., no ties. Although this argument is true, this statistic is meaningful here as it is a good measure to compare the effectiveness of the two different pointawarding schemes on the originally intended effect. The rule change in the Swiss NL mimics all mentioned rule changes in the N H L and additionally introduces the three-point rule. Theoretically, element 1 should counter-balance the effect that more games reach overtime. This is exactly what can be found in the data of the two divisions of the Swiss NL. Table 2 summarizes the figures for the NLA and the NLB. 1 3 10

11 12 13

N o t e that in the post-change period ( 2 0 0 5 - 2 0 0 6 to 2 0 0 8 - 2 0 0 9 ) the shootout rule became effective in the N H L . There are no tied games anymore. But our focus lies on the game status before the shootout. Games ending in a tie after the five-minute overtime play are still possible. The difference is statistically significant with a p - v a l u e < 0 . 0 1 . The difference is statistically significant with a p - v a l u e < 0 . 0 5 . The N H L data is available o n the NHL's w e b page (www.nhl.com). Match data for the N L A and N L B was provided by Christian Wassmer and Martin Merk (www.hockeystats.ch). One game was excluded due to missing data in the N L A and no games were excluded in the NLB and N H L for this statistic. A comment is needed concerning the observed data from the Swiss N L during the 2 0 0 4 - 2 0 0 5 season. Between 3 0 to 4 0 N H L players played several games or that whole season in the Swiss N L due to the N H L lock-out in 2 0 0 4 - 2 0 0 5 . Among them, there have been several w h o could be considered ' N H L stars' (e.g., Joe Thornton, Rick Nash, Martin St. Louis, Danny Heatley, Daniel Brière, Olli Jokinen, Niklas Hagman, Alex Tanguay, Rod Brind'Amour, Jean-Pierre Dumont). Despite the fact that this situation was uncommon, it has not changed the studied issues. The stated results and conclusions based on the descriptive statistics and the probit estimations do not change when season 2 0 0 4 - 2 0 0 5 is excluded from the analysis of the N L A and the NLB.

One for Sure or Maybe Three · 217

Table 2 Game statistics for the NHL, the NLA and the NLB

NHL Observed games % of games going into OT % of OT games ending in a tie NLA Observed games % of games going into OT % of OT games ending in a tie NLB Observed games % of games going into OT % of OT games ending in a tie

Old Rules

New Rules

Absolute Change

Relative Change

2,173 20.34 % 73.98%

4,920 22.68 % 55.91 %

+2.34% pt. -18.07% pt.

+11.50% -24.43%

1,367 18.65% 69.41 %

864 18.63 % 53.42 %

-0.02% pt. -15.99% pt.

-0.11% -23.04%

1,101 15.62 % 62.21 %

864 15.86% 47.83 %

+0.24% pt. -14.38% pt.

+1.54% -23.12%

In the NLA, the percentage of games reaching overtime insignificantly decreased from 18.65 % to 18.63 % after the rule change. Therefore, the probability of a game reaching overtime has not been affected by the rule change. In this sense, the given numbers support the theoretical predictions that the introduction of the three-point rule let the portion of overtime games be stable. At the same time, the percentage of overtime games ending in a tie decreased from 69.41 % before the rule change to 53.42 % afterwards. This corresponds to a relative decline of more than 23 %, which is statistically significant (with a p-value

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Inner-Outer Lane Advantage in Olympic 1000 Meter Speed Skating · 2 9 9

Salt Lake City

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Figure 2 Box plots of the finishing times of the 2001 - 2 0 0 2 events organized in Salt Lake City and Oslo. T h e third box plot in both panels corresponds to pooled (combining Salt Lake City and Oslo) finishing times. (+ indicates outliers)

4

Detecting outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results that deviate from normal performances. It is necessary to eliminate these outliers before the value of the parameter δ is estimated. In order to eliminate races with falls and slips, we introduce bounds on the 1 0 0 0 m finishing times, together with an outlier test. In Section 5 . 2 we show that our results are robust to deleting outliers. 4.1 B o x plots By introducing bounds on the 1 0 0 0 m finishing times, based on b o x plots of the F i n i s h ^ values, we remove races containing a fall or slip. However, b o x plots of pooled finishing times neglect technological progress of equipment, and the fact that races are skated on different rinks. For example, during the season 2 0 0 1 - 2 0 0 2 , Salt Lake City hosted the O G , while W C ' s were organized in Salt Lake City but also on outdoor low-altitude ovals, like the one in Oslo. Drawing conclusions based on such b o x plots of the pooled data o f the season 2 0 0 1 - 2 0 0 2 would lead to the removal of a considerable amount of finishing times (see Figure 2). There are several outliers in the third b o x plot in the two panels of Figure 2 , although the first two plots in both panels contain no outliers. Therefore, we construct b o x plots o f 1 0 0 0 m times from the same rink and the same season. If a finishing time is an outlier in a particular b o x plot, the corresponding bound is lowered and the finishing time is removed. This procedure is repeated until there are no outliers left. 4 . 2 O u t l i e r test In this section we use the same test statistic for the detection of outliers as in H j o r t ( 1 9 9 4 ) and Kamst et al. ( 2 0 1 0 ) . The test statistic reads

300 · Richard Kamst, Gerard H. Kuper, Gerard Sierksma, and Bertus G. Talsma

where F i n i s h ^ denotes the z'th estimated 1000m time of skater c on rink k during season /, and is defined by 9 — ^ ^ 1 9 ^ Λ λ Finish,,,*. = ä + 6 + Season „•,/?, + ^ Rink c , m y m + V S . (5) c

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Estimation results

In this section we present the estimation results from the fixed effects model. Appendix tests the validity of the fixed effects model by comparing it to the random effects model. We test whether there is a difference between starting in the inner or in the outer lane. To that end, we estimate the parameter δ in model (2). In order to test the influence of removing outliers on the results, we apply different values of the bound corresponding to the test statistics. We also give estimates of δ for different bound values. 5.1 Estimates of the fixed effects model

After removing times of races containing an error from the data set mentioned in Section 3.1, 2 6 9 7 and 2529 observations for men and women, respectively, remain. The percentage of removed times of the original data set is 5.70 and 4.57, respectively. Table 2 presents the estimates of the parameters of model (2), the robust standard errors, and the 95 % confidence intervals. Primarily, we are interested in the estimated value of τ— Ο kO τIN ΓΜ •Φ σι (Ν m m •Ί- ιη Τ- kO o o kO 00 σ; m οπ kO 00 ΓΜ σι IV o q τ- Ο Ο o ö Ο ο ο ο Ο ο οι o o o V

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302 · Richard Kamst, Gerard H. Kuper, Gerard Sierksma, and Bertus G. Talsma

trast to indoor rinks, conditions regarding wind and temperature play a vital role on outdoor rinks. This fact is confirmed by the positive and significant estimated values of the parameters of the outdoor rink indicators, except for the high altitude rink in Collalbo. Moreover, the estimates of ß 2 and ß u , corresponding to the ovals in Calgary and Salt Lake City, have negative values and are significant at 95 % . This means that skaters are faster on these rinks than on the oval in Berlin. The reason is that Calgary and Salt Lake City are more than one kilometer above sea level (see Table 1).

5.2 Robustness with respect to outliers Outliers may affect the estimated value of c b e i n g a r a n d o m v a r i a b l e f o l l o w i n g t h e d i s t r i b u t i o n a>c ~ (0, σ ^ ) . N o t e t h a t ή = 0 i m p l i e s t h a t t h e e x p l a n a t o r y v a r i a b l e s a r e u n c o r r e l a t e d w i t h t h e i n d i v i d u a l e f f e c t 0C. T h e test of u n c o r r e l a t e d r e g r e s s o r s a n d i n d i v i d u a l r e g r e s s i o n t e r m s boils d o w n t o t e s t i n g t h e null h y p o t h e s i s Ho : ή = 0 a g a i n s t t h e a l t e r n a t i v e H ^ : η φ 0. B o t h t h e r a n d o m e f f e c t s m o d e l a n d M u n d l a k ' s m o d e l a r e e s t i m a t e d . T h e l a t t e r m o d e l is used f o r t e s t i n g w h e t h e r o r n o t t h e a s s u m p t i o n of u n c o r r e l a t e d r e g r e s s o r s a n d i n d i v i d u a l e f f e c t s h o l d s . T o t h a t e n d , w e e s t i m a t e t h e m o d e l b a s e d o n t h e d a t a set t h a t is o b t a i n e d a f t e r r e m o v i n g o u t l i e r s b a s e d o n b o x p l o t s , a n d n o t o n test statistics. T a b l e A l gives t h e e s t i m a t e s of b o t h m o d e l s . Actually, t h e M u n d l a k m o d e l ( A . l ) is a n e x t e n s i o n of m o d e l (2), o b t a i n e d by a d d i n g t h e t i m e a v e r a g e s of t h e r e g r e s s o r s of m o d e l (2) t o t h e set of r e g r e s s o r s . So t h e n u m b e r of r e g r e s s o r s in m o d e l ( A . l ) is l a r g e r t h a n in m o d e l (2). T h e s e c o n d c o l u m n of T a b l e A l c o n t a i n s t h e r e g r e s s o r s f r o m m o d e l (2) and model (A.l), a n d the third c o l u m n shows where the regressors refer to. N o t e t h a t t h e r e g r e s s o r ¡, c o r r e s p o n d i n g t o t h e c o n s t a n t s , is a n a l l - u n i t vector. C o m p u t i n g t h e t e s t s t a t i s t i c , c o r r e s p o n d i n g t o test t h e null h y p o t h e s i s Ho : ή = 0 a g a i n s t t h e altern a t i v e Η Λ : ή -φ 0, t h e so-called W a l d test (see C a m e r o n / T r i v e d i 2 0 0 7 ) , yields v a l u e s of 3 2 0 . 6 0 a n d 1 9 9 . 3 7 f o r m e n a n d w o m e n , respectively. T h e W a l d statistic h a s a C h i - s q u a r e d i s t r i b u t i o n w i t h 2 7 d e g r e e s of f r e e d o m , b e c a u s e w e a r e t e s t i n g w h e t h e r o r n o t 2 7 p a r a meters are significantly different f r o m zero, simultaneously. Obviously, the null hypothesis is r e j e c t e d in b o t h cases. T h i s i m p l i e s t h a t t h e a s s u m p t i o n of t h e r a n d o m e f f e c t s m o d e l t h a t t h e r e g r e s s o r s a r e u n c o r r e l a t e d w i t h t h e i n d i v i d u a l specific e f f e c t , is n o t v a l i d . So, w e c o n c l u d e t h a t t h e i n d i v i d u a l e f f e c t s s h o u l d be m o d e l e d w i t h a f i x e d e f f e c t s m o d e l .

Inner-Outer Lane Advantage in Olympic 1000 Meter Speed Skating • 305

Tt in 00 τι· 00 Ττ— Ο

τ- 00 σ> σ\ ΙΌ 00 τ- ιό m σι σ> Γν ΓΜ (Ν m (Ν Tt Γη Τ- IV m Τ- ΓΜ (Ν ΓΜ ΓΜ ΓΜ ΓΜ Τ- ΟΝ τ- Τ— Τ— τΟΟ ο Ο ΟÒ ΟΟ ÖΟο ο Ο

ο m ΤΟ

>.0 ιη m ιη ΓΜ το Ο

VC 00 m ^ m VÍJ 00 ΓΜ Γ Μm ΐ in ΓΓΜ τ- Τ- Τ- m — Ö ΟΟ ΟΟ ο ο

m m m σ> 00 τ—*— o οσ ο

m 00 m ΓΜ1 τ— I- Τ-

T3

^Ο σ\ m 00 ιν o ο co ο ο ιν E o §

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ιη 00 ο (Ν m m m 00 ο 00 οο m (Ν ΓΜ ιη Γ- Ο Tt ο ο' ο ο τ ΓΜ

— τ- ιό Ο fx σ> m ΓΜ Iß co ΓΟ m m σι ΓΝ m τ ο ιη ο ΙΌ 'S" Ο ο Ο m m O in in 00 ο ο ΓΝ σ ιο Ο ω σ\ ιη ιη Ν ΙΌ in Tt CMO ΙΌ in O IV ΓΜ τ- Ν τ— ο ο ο ο ο o V ο1 Ο in ΓΜ ΓΜ ο ο Ο m' (Ν

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_2 Ό C 3 2 C 0)

τ- ο co ΓΜ IV 00 σ\ ιη σ\ σ σι Ο m ιη m 00 (Ν ΙΌ τ— ο ΓΜ ιη VD ο Ο τ— ο - i Ο ΙΌ σ> m ιη IV ιη ιη ΓΝ Ο Ο Ο V ΓΜ Ο Ο ο ο ο 4 τ— ο

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s

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m οο m 00 ο m ο τ- τοΟ Ο

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m τ* ΙΌ τΓΜ •se τ— ο ο ΓΜ m οο ο ο

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ΙΌ Γν ΓΜ Ο 00 ΙΌ ΓΜ ο ΓΜ 00 ΓΜ Ο τ— τ— ΓΜ ΓΜ 00 ιη τ— σ\ 00 00 00 σ\ τ- τ- τ- τ- τ- Ο τ- τ- ο ο ο Ο τΟ Ο Ο Ο Ο Ο Ο Ο ο ο ο ci Ο Γν σ IV ΙΌ τ- ιη τ- 00 ΓΜ ΙΌ ΓΜ σ ΓΜ ο τ— >Ό Γν σ ο τ— V τ— V ο

IV ο τΟ

σ m m o

m ιη σι 00 m Τ- Τ- o Ο Οο

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ιη 00 ΓΜ m σ> ΓΜ ττ— ΓΜ τ— οο σι 00 Ο τ- τ- τ- ο ΓΜ ο τΟΟ Οο ο ο Ο m m IV rri

m ιο ΓΜ m τ- τΟ Ο

ν

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5 — o a ° ¿ g -ι

O) > o t

fNfnt«iVCN(0 O O NfntiPONtogi V (ljtìifl>QjajQj H í í ^ S ^ ^ ^ ^ C C C— C C C C C C C C C C C.—C._C C C __ . ._ C C C C C C C C

60

0)

te.

ιη ΓΜ ο ο

τ- V0 IV ιη τ— οο τ— ΓΜ ΓΜ ΓΜ ΓΜ σι Ο ο ΓΝ ο Ο ο

υ S

ιη 00 τ— ΓΜ 00 Ο σ\ σ Ö ο ο

m o 00 IV ο ΙΌ IV ΓΟ ΓΜ o ΓΜ T— σι σ m ΓΜ σ\ 00 •ST o O IV ΓΜ ΓΜ IV ο ο co σ V o O m ΓΜ τ- ο ο Ö

τ- ΓΜ m τin mm ΓΜ m ΓΜ τ— o Ο ΓΜ ΓΜ ΓΜ τ00 m IV ΓΜ σ ο m ιη ο Ο Ο O O Ö o ΓΜ τ— ο τ— ο ο

ιη ΙΌ IV 00 σ\ ΓΜ m ο ο Ο ο ο ο ο ο ο ο δ ο ο ο ο ο ΓΜ ΓΜ ΓΜ ΓΜ ΓΜ ΓΜ ΓΜ ΓΜ • « s ΙΛ l/l Μ m 4 ιη ώ IV οό , ç «~t « CCο Γ ο ο ο ο ο ο o t ^ OOο Ο ο ο ο ο ο ο ο ΓΜ ΓΜ ΓΜ ΓΜ ΓΜ ΓΜ ΓΜ ΓΜ

ο ιη ΤΟ

NW^lfl'ÍNMJlwwrt-ifiinNMΟ f l Τí i- -Ι Ν r rΙ Ίr Ίi Ι- Π r rΦr Ν - rΟvΙ ·^

ΓΜ m ο Ο ο ο ΓΜ ΓΜ τ- ΓΜ Ο ο Οο ΓΜ ΓΜ

ΓΜ ΓΓ) c C ΙοΛ ΙΟ Λ Λ 0 of the initial revenues. With a Champions League, the expected total revenues of club i in country c thus equal

Rci = (1 + k){Dc¡

- ktci )tcl

+ „ % t Fe . Lk L·/ hi

(9)

O f course, not all teams in a national competition participate in a Champions League. Hence, not all teams will see their revenues increase by a constant factor. Therefore, we should interpret λ as an expected value: on average, due to the existence of a Champions League, teams will see their expected revenue increase by a factor λ. Admittedly, this is a shortcut. Teams with more talent will have a better chance of reaching the Champions League and obtaining the additional revenue. T h a t suggests that λ should also depend on the amount o f talent in a team. For ease of analysis, we abstract from that. N o t e moreover that (9) still implies that strong-drawing teams benefit more in absolute value from a Champions League then weak-drawing teams do, as strong-drawing teams do have higher revenues. Also, the probability of winning the Champions League and earning prize money FE does depend on tc ¡. Hence, at least implicitly, we do allow for the fact that strong-drawing teams with more talent expect to earn more in a Champions League. Maximizing profits, a club will solve the following first-order condition:

(1 + X)(Dci

- 2kta )

= "V

+

By definition, the total amount of amount talent in the world is Ew = implies that we can rewrite this condition as

(1 + À)(Dc i - 2kta )

J ^ · tc ¡, which

= wc .

This implies

,

Fe /Ew

-w

+ ( 1 + Á)DC

2k(l+A)

+F

E

(10)

/El

Total demand for talent in country c equals tq . Equilibrium on the market for talent agent requires T" c = EC = Σ , tq, which implies that equilibrium wage rate has to solve

nFE /Ew

- nw + (1 + À)DC

2k(l+l)

+ F

E

/Ei

_ c

-

-

Rewriting yields

...nc

n

Ew — Ec F + E nEl

(l+X)(Dc -2kEc )

(\-Ec IEw )^+{\+X){Oc -2kEc ).

(11)

The Effects of Institutional C h a n g e in European Soccer · 327

Comparing this to (4), we first of all have that wages increase by a factor 1 + λ: as productivity increases by this amount, so does the price of the production factor in a competitive market. Moreover, clubs are willing to pay an additional amount which can be interpreted as follows. First, FE/EW is the total amount of prize money in the Champions League per unit of talent in the world. It can be interpreted as the additional wage that soccer talent would earn due to a Champions League, if it were able to fully appropriate all the prize money. This, however, is not the case. For the sake of argument, suppose that an average team in a country would have all the soccer talent in the world, so EC = EW. Such a team would be certain to win the Champions League, hence it has full bargaining power vis-a-vis its players and does not have to pay them anything extra. In that case, the first term is zero. Now suppose that an average team in a country has an amount of talent that is negligible relative to the world total, so EC/EW = 0. Such a team would have no bargaining power, and would have to pay its talent its full share of Champions League prize money, which equals FE/EW. Inserting (11) into (12), we obtain after some further manipulations: tct_T

, (l+A)(De, - D t ) £ ¿ ik(i + A)EI + Fe •

(iZ)

Substituting this into (1), we obtain

P

"

_ta Ec

1 «

Dc,-Dc 2kEc

(l+A)El

(l+X)Ej + FE/2k-

[

1

Compared to (5) the last term is additional and reflects the effect of a Champions League. We can now show the following: Theorem 3 Consider the introduction of a Champions League in a world without international trade in soccer talent. That introduction will increase competitive balance in all countries. Wages will increase. This is a surprising result, that runs counter to the fears cited in the Introduction. The intuition is as follows. First, we can see from the proof of the theorem that a Champions League would not have an effect on domestic competitive balance if prize money was zero, so Fe = 0. In other words, the fact that the Champions League allows all clubs to increase their gate revenue does not affect competive balance. Marginal revenue of all clubs increases by the same factor, which implies that the allocation of talent is unaffected. The only effect is an increase in the wage rate of talent. Yet, this picture changes if there is prize money involved. Prize money is the same for all clubs, regardless of their drawing power. All clubs therefore have the same incentive to try to win that prize money. This implies that drawing power becomes less important in the domestic allocation of talent. In turn, this implies more competitive balance in the national competition. In this section, we only studied the introduction of a Champions League in a world without international transfers. To fully assess the effects of a Champions League, we need to allow for such transfers as well. In the next section, we therefore study a world with both international trade and a Champions League.

328 · Marco Α. Haan, Ruud H. Koning, and Arjen van Witteloostuijn

5

Scenario 4: International trade, Champions League

We now consider a world in which both international trade is possible, and a Champions League exists. The set-up of the model is identical to that in the previous section, with team revenues given by (9) which implies a demand for talent given by (10). But equilibrium on the labor market requires that the world demand for soccer talent equals the world supply, so we need mnFE/Ew

- mnw + (1 + À)DW _

2k(í+X)+FE/Ei

-

Solving for the equilibrium wage rate then yields: wtc=

( mnj Ew

\

l

V

-

)

—

(

1

4

)

This expression is similar to (11), but again with the international club averages replacing the national club averages. Note that in (11 ), we had the term EC/EW, the fraction of the talent of the average club in country c relative to total talent in the world. Now we have the fraction of the talent of the average club in the world relative to total talent in the world. By construction, this simply equals 1 /mn. Solving for tc¡ yields ÎC_=

* " -

(1 +

λ)Εΐ(Ρα-Έ)

2k(í

Ε +

+X)EI

+ FE

•

( 1 5 )

The amount of talent that is hired by teams in country c equals

c

2k

+

(l+A)Ei

+ FE/2k·

( i b )

The probability that team i will win its national competition now equals ,;„ Vc'

tt Τ*

' η

(l+A)g(De,--De) (l+A)Ei(2kE + Dc-D)+FEE'

1

'

For the results that follow, we need to put a mild restriction of prize money FE. For the remainder of this paper, we will assume the following: FE < Ew(l

(18)

+ À)(DW — 2kEw).

To interpret this inequality, first note that the total worldwide wage bill in the case that FE = 0, equals Ew • wtc = Ew{ 1 + λ) (θ - 2kT)

= Ew{ 1 + λ)(DW -

2kEw)/mn.

Condition (18) then implies that total prize money in the Champions League per existing club does not exceed the total worldwide wage bill from sources other than prize money in the Champions League. It is clear that this is a very mild assumption. We can now show:

The Effects of Institutional Change in European Soccer • 329

Theorem 4 In a world with a Champions League, consider a move from autarky to one with international trade in soccer talent. Such a move will lead to a net flow of talent from small to big countries. Hence quality differences between national competitions will increase. Wages increase in small countries, and decrease in large ones. Competitive balance will increase in large countries, but will decrease in small countries. Note that these results are equivalent to those in Theorems 2 and 1, and hence are invariant to the existence of a Champions League. Again, as borders open, production factors flow to where they have the highest productivity, i.e. to countries with a high demand for soccer. Again, competitive balance increases in strong countries, as the relative distribution of talent in these countries improves, while competitive balance decreases in weak countries, as the relative distribution of talent deteroriates in these countries. So far, we have only considered the introduction of international trade in a world with a Champions League. Yet, our results also allow us to study the effect of the introduction of a Champions League in a world with international trade. We can then show the following: Theorem Sina world with international trade in soccer talent, consider the introduction of a Champions League. Such a move will increase competitive balance in all countries. Wages will increase. Talent will flow from large countries to small countries. Hence, international quality differences will become smaller. Again we have that the introduction of a Champions League will increase competitive balance in national competitions. The intuition for this result is the same to that of Theorem 3. The effect on international quality differences is particularly surprising. The intuition for that result is very similar to that of Theorem 3. In a world without a Champions League, the earnings potential for teams from small countries is almost negligible. Hence, they have little incentive to attract talent. But with the introduction of a Champions League, such earnings potential does exist. This gives those clubs an incentive to at least have a shot at trying to win some of the money involved. Of course, the same is true for clubs in large countries, but for them, prize money in the Champions League is relatively less important. As a result, some talent will flow from large countries to small countries. Above, we looked at the partial effects of the Bosman ruling (modelled as the introduction of international trade) and the introduction of the Champions League. This still leaves the combined effect of these institutional changes undetermined. For example, we saw that starting from autarky, introducing international trade increases international quality differences, but introducing a Champions League decreases them again. Also, in small countries introducing international trade decreases competitive balance, but the Champions League increases it again. In both cases, the net effect is not entirely clear. We can however prove the following: Theorem 6 Consider a move from autarky without a Champions League, to a situation with international trade in soccer talent, and a Champions League. Such a move will lead to a flow of talent from small countries to large countries. Wages increase in small countries, and decrease in large ones. Competitive balance increases in large countries. It also increases in some small countries, but will decrease in the smallest ones. Thus, the talent flow caused by the introduction of international trade always dominates that caused by the introduction of a Champions League. For small countries, international trade decreases competitive balance, but a Champions League increases it. For

330 · Marco A. Haan, Ruud H. Koning, and Arjen van Witteloostuijn

the smallest countries the trade effect dominates, while for somewhat larger countries, the Champions League effect does.

6

Summary and conclusion

Using a theoretical model, we studied how the introduction of international trade in soccer players, and the introduction of the Champions League, has affected competitive balance within national competitions, and quality differences between national competitions. Our main results are summarized in Tables 2 and 3. First, introducing international trade in talent leads to a flow from small countries to large ones. As the returns to talent are higher in large countries, more talent will be employed there. As a result, wages will increase in small countries, but decrease in large ones. In small countries, the wage increase hurts all teams, but it hurts small teams relatively more than large ones. Therefore, competitive balance will decrease. In large countries, small teams benefit more from the wage decrease than large ones do, and competitive balance increases. These results are independent on whether or not a Champions League exists. The introduction of a Champions League implies the possibility for teams to win a large amount of prize money. This possibility is relatively more important for small teams. Hence, competitive balance increases in all countries, and talent flows from large to small countries, provided of course that international trade in talent is possible. Wages increase. Table 2 The effect on international quality differences initial situation

introducing trade

introducing CL

introducing both

no trade, no CL

increase

no effect

increase

no trade, CL

increase

trade, no CL

decrease

Table 3 The effect on competitive balance initial situation

introducing trade

introducing CL

introducing both

no trade, no CL

increases in big countries, decreases in small countries

increases in all countries

increases in most countries but decreases in very smallest

no trade, CL

increases in big countries, decreases in small countries

trade, no CL

increases in all countries

The Effects of Institutional Change in European Soccer · 331

When we study the joint implementation of both international trade in talent and a Champions League, we find that talent flows from small to large countries. Hence, as far as the international distribution of talent is concerned, the trade effect dominates the Champions League. Competitive balance increases in all but the very smallest countries, where it will decrease. Of course, any model is only as good as its assumptions. First, we assume that revenues are only affected by absolute qualities, not by relative qualities. This greatly simplifies the analysis, while we do not believe that changing this assumption would affect the qualitative results. Second, we assume that the presence of a Champions League increases the revenues from merchandising and the like by a factor that is constant for all teams. Of course, one could argue that teams with a strong drawing power benefit more than proportionally from a Champions League. If that effect is strong enough, it may at some point overturn the positive effect on competitive balance that we predict. Third, we assume that the amount of talent is fixed. If a wage increase would increase the supply of talent, then this would partly offset our results on the international distribution of talent. But it would not affect our qualitative result as long as the supply of talent is not infinitely elastic. Based on our analysis, not all fears that we cited in the introduction are justified. Our results suggest that an increased mobility of players will indeed lead large countries to increasingly dominate European competitions. But competitive balance within national competitions will increase, albeit only in large countries. Furthermore, our results suggest that the Champions League in itself with lead to more competitive balance, both nationally and internationally. However, the latter effect is dominated by that of increased player mobility. Based on our model, the " 6 + 5 " rule mentioned in the introduction is easy to analyze as well. That rule will decrease player mobility. On the basis of our analysis, that would imply that wages will decrease, that competitive balance will increase in small countries, but that it will decrease in large ones. International quality differences will decrease. Whether this is desirable from a welfare point of view, is debatable. Arguably, if fans in large countries are willing to pay more to watch soccer talent, it would be efficient to allow them to do so.

Appendix: Proofs Proof of Theorem 1 Note that p"" = p'" = 1/n if Da = Dc, so we can apply Lemma 1. Competitive balance increases if dp%/dDci < dp™/dDa or if 1 2k l + D

1 c

- D


dp""/dDci, and competitive balance decreases.

332 · Marco Α. Haan, Ruud H. Koning, and Arjen van Witteloostuijn

Proof of Theorem 2 From (7), talent flows t o a country whenever Dc - D

^

~2k

>

Suppose, without loss of generality, that a country has Dc = yD. W i t h a proportional endowment o f talent, the inequality then reduces to (γ — 1 ) ( D — 2kE)

> 0.

With D — 2kE > 0 , this is satisfied if and only if γ > 1, i . e . if the country is large. W i t h equal endowments o f talent, the inequality reduces to (y-l)D>0, which again is satisfied if and only if y > 1. For the effect on wage rates, note from (4) and (6) that we can write w

tn

nn

— w

=

D — 2kE

(De - 2kEc)

η

η

1

=

(1 — y ) ( D — 2kE) η

which is positive if and only if y < 1, thus if the country is small.

Proof of Theorem 3 Consider a strong-drawing team, so Dc¡ > Dc. Again using L e m m a 1, we have that c o m petitive balance in the national competition increases if El( 1+λ) 2kEi(l+Á) or

+ FE

1 JU ι

Fe


0. But this is exactly (19), which we k n o w to be true if (18) is satisfied. For the case of an equal e n d o w m e n t of talents, condition (20) reduces to E2Jl+A)(Dc-D)

>0

which is satisfied if and only if Dc > D, i.e. if the country is large.

334 · Marco Α. Haan, Ruud H. Koning, and Arjen van Witteloostuijn

Proof of Theorem 5 Using (8) and (17), we have f r o m L e m m a 1 that competitive balance increases if 1

1

which is always satisfied. The effect on wages follows directly f r o m a c o m p a r i s o n of ( 11 ) and (14). F r o m (7) and (16 ), the net effect of the introduction of a C h a m p i o n s League in country c is Ttc

Ttn


E2W( 1 + Λ ) ( Ρ - 2KE)

-

(1 + X)E2W(DC

- 2KEC)

(21)

Consider the case of p r o p o r t i o n a l e n d o w m e n t s . T h e inequality then reduces to FE > EW(L

— Y)(L + À)(DW

— 2KEW).

(22)

For γ > 1, it is clear that this inequality is satisfied. W i t h γ = 0, it exactly violates (18). With the right h a n d side strictly decreasing in γ, this establishes the result. W i t h equal e n d o w m e n t s , (21) reduces to FE>Ew(l

+

X)(L-Y)DW.

Again, this is clearly satisfied for γ > 1. With γ = 0, it reduces to FE > Ew(l + À)DW, which violates (18). W i t h the right h a n d side strictly decreasing in γ, this establishes the result.

The Effects of Institutional Change in European Soccer · 335

References Buraimo, B., D. Forrest, R. Simmons (2007), Freedom of entry, market size, and competitive outcome: Evidence f r o m English soccer. Southern Economic Journal 74: 204-213. El Hodiri, M . , J. Quirk (1971), An economic model of a professional sports league. Journal of Political Economy 79: 1302-1319. Feess, E., G. Muehlheusser (2003), Transfer fee regulations in European football. European Economic Review 47: 645-668. Feess, E., F. Stähler (2009), Revenue sharing in professional sports leagues. Scottish Journal of Political Economy 56: 255-265. FIFA (2008), Fifa congress supports objectives of 6+5. FIFA, Zurich. Press release, available at http://www._fa.com/about_fa/organisation/bodies/news/newsid=783657/, (webpage dated 30.05.2008, last retrieved 09.02.12). Fort, R., J. Quirk (1995), Cross subsidization, incentives and outcomes in professional team sports. Journal of Economic Literature 33: 1265-1299. Frick, B. (2007), The football players' labor market: Empirical evidence from the m a j o r European leagues. Scottish Journal of Political Economy 54: 422-446. Frick, B. (2009), Globalization and factor productivity. Journal of Sports Economics 10: 88-106. H a a n , Μ . Α., R . H . Koning, A. van Witteloostuijn (2007), Competitive balance in national European soccer competitions. Pp. 63-76 in: J. Albert, R . H . Koning (eds.), Statistical Thinking in Sports. Boca Raton: C R C Press. Késenne, S. (2007), The peculiar international economics of professional football in Europe. Scottish Journal of Political Economy 54: 388-399. Kleven, H., C. Landais, E. Saez (2010), International migration of superstars: Evidence from the European football market. Technical Report 16545, NBER Working Paper. Koning, R . H . (2009), Sport and measurement of competition. De Economist 157:229-249. Rottenberg, S. (1956), The baseball players' labor market. Journal of Political Economy 64: 242-258. Szymanski, S. (2004), Professional team sports are only a game: the Walrasian fixed-supply conjecture model, contest-Nash equilibrium, and the invariance principle. Journal of Sports Economics 5: 111-126. Szymanski, S. (2007), The champions league and the Coase theorem. Scottish Journal of Political Economy 53: 355-373. Szymanski, S., S. Kesenne (2004), Competitive balance and gate revenue sharing in team sports. Journal of Industrial Economics 52: 165-177. M a r c o H a a n , Department of Economics, Econometrics, and Finance, University of Groningen, P.O.Box 800, 9700 AV Groningen, the Netherlands. [email protected] Ruud Koning, Department of Economics, Econometrics, and Finance, University of Groningen, P. O.Box 800, 9700 AV Groningen, the Netherlands. r. [email protected] Arjen van Witteloostuijn, University of Antwerp, Faculty of Applied Economics, Antwerp Centre of Evolutionary Demography, Prinsstraat 13, 2 0 0 0 Antwerpen, Belgium. [email protected]

Jahrbücher f. Nationalökonomie u. Statistik (Lucius & Lucius, Stuttgart 2012) Bd. (Vol.) 232/3

A Contest Model of a Professional Sports League with Two-Sided Markets By Helmut Dietl, Tobias Duschl, Egon Franck, and Markus Lang, Zurich* JEL L11; L13; L83; M21 Competitive balance; contest; multisided market; network externalities; team sports league.

Summary This paper develops a model of a professional sports league with network externalities by integrating the theory of two-sided markets into a two-stage contest model. In professional team sports, the competition of the clubs functions as a platform that enables sponsors to interact with fans. In these club-mediated interactions, positive network effects operate from the fan market to the sponsor market, while positive or negative network effects operate from the sponsor market to the fan market. We show that the size of these network effects determines the level of competitive balance within the league. If the market potential of the sponsors is small (large), competitive balance increases (decreases) with stronger combined network effects. We further deduce that clubs benefit from stronger combined network effects through higher profits and that network externalities can mitigate the negative effect of revenue sharing on competitive balance. Finally, we derive implications for improving competitive balance by taking advantage of network externalities. For example, our model suggests that an increase in the market potential of sponsors produces a more balanced league.

1

Introduction

The professional team sports industry has a unique organizational structure. It is the only industry in which production is organized by leagues. This unique organizational structure is the result of the industry-specific p r o d u c t i o n and competition process. Industry outsiders often tend to regard individual teams as firms a n d treat them as production units. Unlike an a u t o m o b i l e firm, however, an individual team c a n n o t p r o d u c e a m a r k e t a b l e product. Each team needs at least one o p p o n e n t to play a m a t c h . However, even a m a t c h between t w o teams is not an attractive product. The individual matches must be upgraded by integrating t h e m into an organized c h a m p i o n s h i p race. This upgrade, which gives each individual m a t c h additional value within the larger context of the c h a m p i o n s h i p race, is m a n a g e d by the league. * Previous versions of this article were presented at the 86th Annual Conference of the Western Economic Association in San Diego, the 2nd European Conference in Sport Economics in Cologne, Germany and the 10th Annual Meeting of the European Academy of Management (EURAM) in Rome, Italy. We would like to thank two anonymous referees and conference participants especially Harald Dolles, Bernd Frick, Paul Madden, Thomas Peeters, Leigh Robinson and Stefan Szymanski - for helpful comments and suggestions. Financial assistance was provided by a grant of the Swiss National Science Foundation (Grant No. 100014-120503) and the research fund of the University of Zurich (Grant No. 53024501).

A Contest M o d e l of a Professional Sports League with Two-Sided Markets · 337

From a sports perspective, each team within a league wants to win as many games as possible. Economically, however, teams are not so much competitors but are rather complementers. The quality or economic value of the championship race depends to a large extent on the level of competitive balance. Unlike Toyota and Ford, which prefer weak competitors in their industry, sports teams like Real Madrid, the N e w York Yankees, and the Dallas Cowboys benefit f r o m having strong opponents within their leagues. A more balanced league usually produces a more attractive - that is, economically more valuable - product. 1 The clubs' competition provides the platform for the interaction of various market sides such as fans, advertisers and sponsors, the media, and merchandising companies. These interactions via an intermediary platform creates what is called a "multisided market." Each of the distinct market sides demands a specific good or service provided by the intermediary. Frequently, the market sides do not interact with each other directly; however, they exert network externalities on each other. These externalities influence the market's demand structure and the intermediary's pricing schemes. Fans demand competition and the experience of a sports event, advertisers and sponsors demand an audience that they can inform about their products or services, the media demand an audience willing to pay for the use of their services, merchandising companies demand customers w h o want to buy their articles, etc. An interaction between two market sides only takes place because of the underlying sports event. Fans would hardly consume advertisement content if there were not a match taking place that featured their favorite team. Merchandising companies would sell many fewer fan articles if their products were not linked to an active sports team, and so on. These examples underline the importance of the clubs' competition to act as a platform for the different market sides that interact and exert network externalities on each other. We add to the literature by contributing to two different strands of literature: on the one hand, the literature on multisided markets and on the other hand, the literature on analytical models of sports leagues. To the best of our knowledge, we are the first to integrate the theory of two-sided markets into a contest model of a professional team sports league. 2 Our model can then be used as a basic framework to analyze the effect of different cross-subsidization schemes in team sports leagues. In particular, this paper develops a model of a professional sports league with network externalities by integrating the theory of two-sided markets into a two-stage contest model. In professional team sports, the competition of the clubs functions as a platform that enables sponsors to interact with fans. In these club-mediated interactions, positive network effects operate from the fan market to the sponsor market, while positive or

1

2

According to the so-called "uncertainty of outcome" hypothesis (Rottenberg 1956), fans prefer to attend games with an uncertain outcome and enjoy close championship races. For empirical contributions that analyze the relation between competitive balance and match attendance, see Downward and Dawson (2000), Borland and MacDonald (2003) and Szymanski (2003). Notable exemptions include Bae and Kwon (2008) and Budzinski and Satzer (2010). Bae and Kwon (2008) present an analytical model in which teams in a sports leagues compete for players and fans. In their framework, two-sided network effects are important because a club with a larger portion of talented players attracts more fans and, simultaneously, players want to play for a large-market club. However, they do not explicitly model the competition of the clubs via contest theory. Budzinski and Satzer (2010) develop a conceptual framework by describing the platform elements of professional suppliers of sports events.

338 · Helmut Dietl, Tobias Duschl, Egon Franck, and Markus Lang

negative network effects operate from the sponsor market to the fan market. 3 In line with standard results in the literature on two-sided markets (Armstrong 2 0 0 6 ; Kaiser/Wright 2 0 0 6 ; Rochet/Tirole 2 0 0 6 ) , we derive that clubs react to stronger fan-related network externalities by charging lower prices to fans and higher prices to sponsors. T h e opposite holds true for weaker negative or stronger positive sponsor-related network externalities. N e w and potentially important for professional sports, our analysis further shows that the size of these network externalities determines the level of competitive balance within the league. Depending on the market potential of the sponsors, competitive balance increases (small market potential) or decreases (large market potential) with stronger combined network effects. Moreover, we show that clubs benefit from the presence of network externalities because club profits increase with stronger combined network effects. The paper can be of interest to policy-makers in a professional team sports league because we derive recommendations of how to improve competitive balance by taking advantage of network externalities. Our model suggests that an increase in the market potential of sponsors produces a more balanced league because the small club will increase its talent investments more than the large club in equilibrium. Finally, we show that network externalities can mitigate the negative effect of revenue sharing on competitive balance. Taking a closer look at major team sports leagues worldwide, one can find a number of phenomena that may be explained by our model. For example, the differences in match attendance and average ticket prices between national leagues in European football are accompanied by strong divergences in sponsor-related revenues. While match-day income (e.g., ticket sales and others) in the 2 0 0 8 / 2 0 0 9 season with € 6 6 5 m was higher in the English Premier League than in the German Bundesliga, where it amounted to € 3 6 3 m , a look at commercial revenue (e.g., sponsorship and others) yields the opposite picture, there, the Premier League generated € 5 2 7 m and the Bundesliga € 7 2 3 m (see Deloitte & Touche 2 0 1 0 ) . This observation provides anecdotal evidence for our theoretical model and mirrors the trade-off between fan-related and sponsor-related revenues. T h e quota for sponsorship in many North American m a j o r leagues represents another example; even though teams might be able to obtain higher revenues by increasing the amount of sponsoring/advertisements, the majority of teams refrains from posting advertisements on jerseys. 4 The paper is structured as follows. Section 2 reviews the related literature. In Section 3 , we present our model with its notation and main assumptions. We specify fan and sponsor demand, the quality of the competition and club profits. In Section 4 , we solve the two-stage game, derive the subgame-perfect equilibria and discuss the results. Section 5 highlights policy implications regarding competitive balance and revenue sharing. Finally, Section 6 points out possible extensions and concludes the paper. 2

Literature review

Economists have designed various models of sports leagues. In an early contribution, El-Hodiri and Quirk ( 1 9 7 1 ) developed a dynamic decision-making model of a profes3

4

See Becker and Murphy ( 1 9 9 3 ) for a discussion on advertisements as a good or bad. For further analysis of advertisements see, e.g., Depken and Wilson ( 2 0 0 4 ) and Reisinger et al. ( 2 0 0 9 ) . N o t e that teams in the National Football League (NFL) are allowed to post a sponsor on their jerseys. Only a small proportion of teams, however, makes use of this opportunity.

A Contest Model of a Professional Sports League with Two-Sided Markets · 339

sional sports league and incorporated certain f u n d a m e n t a l features of the N o r t h American sports industry such as the reserve clause, player drafts and the sale of player contracts a m o n g teams. They show t h a t revenue sharing does not influence competitive balance a n d thus confirm the "invariance p r o p o s i t i o n " . 5 Fort and Q u i r k (1995) derive similar results in an u p d a t e d , static version of the El-Hodiri and Quirk model. Atkinson rt al. (1988) contradict the invariance proposition and s h o w that revenue sharing can improve competitive balance. In their model, Atkinson et al. a d o p t a pool-sharing arrangement a n d a club revenue function t h a t depends on the team's p e r f o r m a n c e and on the p e r f o r m a n c e of all other teams. Their result is supported by M a r b u r g e r (1997), w h o builds his model on the assumption that fans care a b o u t the relative and absolute quality of teams. V r o o m a n (1995) shows t h a t sharing the winning-elastic revenue does not affect competitive balance, while sharing the winning-inelastic revenue does improve competitive balance. Késenne (2000a) develops a t w o - t e a m model consisting of a large- and a small-market club and shows that a payroll cap, defined as a fixed percentage of league revenue divided by the n u m b e r of teams, will improve competitive balance as well as the distribution of player salary within the league (Késenne 2007). The recent sports economics literature has suggested modeling a team sports league by m a k i n g use of contest theory. 6 In his seminal article, Szymanski (2003) applied Tullock's (1980) rent-seeking contest t o ascertain the optimal design of sports leagues. Based on a model of t w o profit-maximizing clubs and a club revenue function that depends on the relative quality of the h o m e team, Szymanski and Késenne (2004) show that gate revenue sharing decreases competitive balance. This result is driven by the so-called "dulling effect." T h e dulling effect describes the well-known fact in sports economics that revenue sharing reduces the incentive t o invest in playing talent. Dietl a n d Lang (2008) confirm this finding and f u r t h e r show that gate revenue sharing increases social welfare. As this brief review of the sports economics literature shows, analytical models in sports are mainly focused on the effect of cross-subsidization schemes such as reserve clauses, revenue sharing and salary caps on competitive balance w i t h o u t taking into account that the competition of the clubs provides the p l a t f o r m for the interaction of various m a r k e t sides (fans, sponsors, advertisers a n d the media). These club-mediated interactions of different m a r k e t sides create a "multisided m a r k e t . " Research related to multisided markets is flourishing and has been conducted o n a broad range of topics and industries: e.g., software p l a t f o r m s (Evans et al. 2004), p a y m e n t systems (Rochet/Tirole 2002; Schmalensee 2 0 0 2 ; Wright 2 0 0 3 , 2004), the Internet (Baye/Morgan 2 0 0 1 ; Caillaud/Jullien 2003) a n d media markets (Kaiser/Wright 2006; C r a m p e s et al. 2 0 0 9 ; Reisinger et al. 2009). M o r e general models have been proposed by Rochet and Tiróle (2003b), Armstrong (2006), Armstrong a n d Wright (2007) and Belleflamme a n d Toulemonde (2009). The analysis of two-sided markets d r a w s on the literature on n e t w o r k externalities and multi-product pricing (Rochet/Tirole 2006). Pricing decisions account for originally non-internalized externalities a m o n g the m a r k e t sides. For example, the m a r k e t side that exerts larger positive externalities on the other m a r k e t side is subsidized via a lower price (see Armstrong 2 0 0 6 ; Kaiser/ 5

6

The "invariance proposition" goes back to Rottenberg (1956) and states that the distribution of playing talent between clubs in professional sports leagues does not depend on the allocation of property rights to players' services. See also Vrooman (1996). The first approaches in contest theory were made by Lazear and Rosen (1981), Green and Stokey (1983) and Nalebuff and Stiglitz (1983).

340 · Helmut Dietl, Tobias Duschl, Egon Franck, and Markus Lang Wright 2 0 0 6 ) . Apart from implications for agent behavior in two-sided markets and optimum pricing decisions, research also has established important implications for economic policy. It has been shown that measures which are conducive in traditional markets may be ineffective or negative in two-sided markets (Wright 2 0 0 4 ; Evans/Schmalensee 2 0 0 5 ) . For example, two-sided markets may show price structures that do not reflect a meaningful economic relationship between prices and costs on either side of the market considered by itself, which matters for antitrust analysis (Evans 2 0 0 3 ; Rochet/Tirole 2 0 0 3 ) . Despite the large variety of applications, the theory of multisided markets has not yet been applied to contest models of professional sports leagues. Our paper tries to fill the gaps in the literature on sports economics and multisided markets by developing a simple contest model of a professional team sports league with two market sides and network externalities.

3

Model setup

We model a professional team sports league with two clubs, denoted as 1 and 2. The clubs are asymmetric with respect to their market size - that is, there is one large-market club and one small-market club. Each club i e { 1 , 2 } invests independently a certain amount x¡ > 0 in playing talent to maximize its profits. 7 Talent is measured in perfectly divisible units that can be hired at a competitive labor market. In our model, the competition of the clubs provides the platform that serves as the intermediary between two groups: fans and sponsors. Fans can consume sports competition by watching a match, while sponsors are attracted to the competition because sports events draw large crowds of potential customers and help to build a positive corporate image. The size of the crowd can then be leveraged through media coverage - an effect that we model indirectly. The attractiveness of a sports event for sponsors increases with the number of fans watching. The presence of sponsors, in turn, may have a negative effect on the attractiveness of the event for the fans. These indirect effects are modeled as network externalities in the sponsor and fan demand functions. The timing of the model features a two-stage structure: 1. Stage: Clubs invest independently in playing talent with the objective of maximizing their own profits. Talent investments determine the win percentages and thus the quality of the competition of the two clubs. 2. Stage: Given a certain quality of competition, clubs charge prices for fans and sponsors taking into account the network externalities that operate from one market side to the other. Next, fans and sponsors make their decisions and each club then generates its own revenues dependent on the decisions of fans and sponsors. In the sections that follow, we derive the demand functions of fans and sponsors under network externalities and specify the quality of the competition. Finally, we derive club revenues, costs and profits.

3.1 Demand of fans and sponsors under network externalities Following the literature on two-sided markets (e. g., Armstrong 2 0 0 6 ) , the linear demand functions are defined as follows. We assume that the fans of club i demand the quantity > 0 given by 7

If not otherwise stated, henceforth / , / e { 1 , 2 } , with i φ j.

A Contest Model of a Professional Sports League with Two-Sided Markets · 341

q{ = m{

+ n*q],

while the amount of advertising q\>0 q] = m

¡

- £ + nfqf¡,

(1)

that sponsors place at club i is given by 8 (2)

with prices p{ > 0, p] > 0, quality of the competition 0, > 0, market sizes mt > 0, m s > 0, and network effects nf G [0,1), η5 G ( - 1 , 1 ) . The price fans have to pay to be able to watch a match, is denoted by while p] stands for the price sponsors have to pay for advertisements. Clubs can charge fans for watching the match by selling tickets and also, indirectly, by collectively or individually selling media rights. Through ticket sales, clubs directly generate revenues from fan attendance. Through media rights sales, clubs indirectly generate revenues from fans by the sale of the rights to a broadcasting company, which in turn charges its viewers for the broadcast. 9 The parameter »«(characterizes the market size of club i. We assume that club 1 is the large club, with a higher drawing potential, and as a result, a bigger fan base than the small club 2, such that > rrl2. Furthermore, the parameter »^represents the total market potential of the sponsors, or, in the case of a binding quota for sponsoring defined by the league, the sponsors' bounded market potential. 1 0 The network externalities that operate from the fan market to the sponsor market are referred to as "fan-related network externalities" and are denoted by nf G [0,1). We assume that the fan-related network externalities are positive because more fans imply more publicity and thus have a positive effect on the demand in the sponsor market. O n the other hand, the network externalities that operate from the sponsor market to the fan market are referred to as "sponsor-related network externalities" and are denoted by n$ G (—1,1). Thus, we allow for positive or negative sponsor-related network externalities. However, we assume that the positive fan-related network externalities are at least as strong as the sponsor-related network externalities in absolute values, i.e., nf > |« s |. The possibly positive (even though small) effect of advertising on consumers (see, e.g., Nelson 1974 and Kotowitz/Mathewson 1979) reduces the negative sponsorrelated network externalities such that the assumption nf > \ns\ is reasonable. 1 1 8

9

10

11

For the sake of completeness, we define the demand function of the sponsors q • to be zero in the case that there are no fans, i. e., qf = 0. However, note that qf = 0 will never be an equilibrium outcome. In a first approach, our model includes the media indirectly as a lever for higher fan attendance. In further research, the media sector could be modeled as a third market side. Note that the parameter ms has no subscript, because we assume that there is only one homogeneous group of sponsors in the league offering advertisements to the two types of clubs. The introduction of a club-specific sponsor with market potential ms- at club i would not change the results qualitatively. A potentially negative externality derived from advertisements could be that fans want to watch sports events, not advertisements. In the case where the actual sports event is adapted to commercial requirements, e.g., special advertisement breaks, this aspect becomes even more obvious. For further discussion of this aspect, see Becker and Murphy (1993), Depken and Wilson (2004) and Reisinger et al. (2009).

342 · Helmut Dietl, Tobias Duschl, Egon Franck, and Markus Lang

In general, network externalities can be illustrated by a displacement of the demand functions q{ and q\. In this respect, stronger network externalities induce stronger displacement of the corresponding demand functions. T h e combined network effects from fans and sponsors, denoted by η are given by η = nf + ns. A higher nf implies that the positive fan-related network externalities are relatively more important than the sponsor-related network externalities, such that the combined network effects increase. Similarly, a higher ns (i. e., either weaker negative or stronger positive sponsor-related network externalities) results in stronger combined network effects. By assuming that nf > \ns\ the combined network effects η are not smaller than zero - i. e., η € [ 0 , 2 ) . Consequently, η > 0 describes a situation with positive combined network effects in which the positive fan-related network externalities are stronger than the sponsor-related network externalities in absolute values. If η = 0 then the combined network effects equal zero. In this case, we have either a situation without network externalities (i.e., nf = ns = 0) or a situation with equalized network externalities in which both individual network externalities are equal in terms of absolute values (i.e., nf = — n$). Finally, the parameter 0,denotes the quality of the competition between club i against club j and is specified below by equation (5). We assume that a higher quality of the the event (competition of the clubs) has a positive effect on fan demand, but at the same time, it has also a positive impact on sponsor demand (i.e., 9q s ¡/W¡ = Pï/ûi + n ^(ô 0 ) : there is a positive effect > 0 through more fans and a positive leverage effect ps¡¡(P¡ > 0 , because a high quality event draws a larger audience. T h e media serve as an additional lever, increasing sponsors' exposure to consumers. 1 2 Consequently, sponsors' demand increases through a higher quality via more media exposure (Borland/MacDonald 2 0 0 3 and Farrelly/Quester 2 0 0 3 ) . 3.2 The quality of the competition We assume that the quality of the competition 9¡ depends on two factors: the probability of club i's success and the uncertainty of outcome. Following Dietl et al. ( 2 0 0 9 ) and Lang et al. ( 2 0 1 1 ) , we further assume that both factors enter the quality function as a sum with equal weights. 1 3 We measure the probability of club i's success by the win percentage w, of this club. T h e win percentage, in turn, is characterized by the contest-success function (CSF), which maps the vector (x¡,xj) of talent investment into probabilities for each club. We apply the Tullock CSF, which is the most widely used functional form of a C S F in sporting contests, and we thus define the win percentage w¡ of club i as 1 4

w¡(x¡,xj) =

Xj -+- Xj

,

(3)

12

According to Grohs et al. ( 2 0 0 4 ) sponsors aim to maximize their media presence and connect the image of their products to the image of the sports club brand in order to increase the demand for their goods and services.

13

We will see below that this specification of the quality function gives rise to a quadratic revenue function widely used in the sports economic literature. This logit CSF for imperfectly discriminating contests was generally introduced by Tullock ( 1 9 8 0 ) and it was subsequently axiomatized by Skaperdas ( 1 9 9 6 ) and Clark and Riis ( 1 9 9 8 ) . An alternative functional form would be the probit CSF (Lazear/Rosen 1 9 8 1 ; Dixit 1 9 8 7 ) , the difference-form CSF (Hirshleifer 1 9 8 9 ) and the value weighted CSF (Runkel 2 0 0 6 ) . See Dietl et al. ( 2 0 0 8 ) and Fort and Winfree ( 2 0 0 9 ) for studies concerning the effect of the discriminatory power in the CSF.

14

A Contest Model of a Professional Sports League with Two-Sided Markets · 343 where χ, > 0 characterizes the talent investments of club i. We define wt(x,, x,) := 1 / 2 if x¡ = Xj = 0. Given that the win percentages must sum up to unity, we obtain the addingup constraint: Wj = 1 — w¡. Following Szymanski (2004), we adopt the "Contest-Nash conjectures" and compute the derivative of equation (3) as dw¡/bx¡ = x¡/(x¡ + x¡)2. The uncertainty of outcome is measured by the competitive balance in the league. Following Szymanski (2003), Dietl and Lang (2008), and Vrooman (2008), we specify competitive balance CB by the product of the win percentages, i.e., CB (x, ,Xj) = w¡ (x¡ ,x¡)· Wj (x, ,Xj)=

X'X' (Xi+Xj)

2

.

(4)

Note that competitive balance attains its maximum of 1 / 4 for a completely balanced league in which both clubs invest the same amount in talent such that — w2 = 1 /2. A less balanced league is then characterized by a lower value of CB. With the specification of the win percentage given by equation (3) and competitive balance given by equation (4), club Γs quality function Θ, as described above is derived as 15 χ (x + 2x•) 0¡{x„xj) = w¡{xi,xj) + w¡{x„xj) [1 - wi{x¡,xj)] = -f—1 {x, + xi)

(5)

A higher win percentage w¡ of club i increases the quality of the competition 9¡, albeit at a decreasing rate, which reflects the impact of competitive balance on the quality of the competition, i.e., 00,/0m/; > 0 and d26¡/dwf < 0. 1 6 3.3 Derivation of club revenues, costs and profits Each club generates its own revenues such that total revenue R¡ of club i is given by the sum of fan-related revenue f/¡qt and sponsor-related revenue p^q]: R. = pW. + PW, = [ H - «7Í + * m\, we must bound ms from above such that ms 0.

A Contest M o d e l of a Professional Sports League with Two-Sided Markets · 345

In line with well-established results from the literature on two-sided markets (Armstrong 2006; Kaiser/Wright 2006; Rochet/Tirole 2006), Part (i) of the lemma shows that the stronger are the positive fan-related network externalities ηί, the higher is the equilibrium quantity demanded by fans and sponsors. If there is a disutility of the sponsors' advertisements for fans (n$ < 0), then the equilibrium quantities demanded by fans and sponsors decrease with stronger, i.e., more negative sponsor-related network externalities. If, on the other hand, ns > 0, then the equilibrium quantities demanded by fans and sponsors increase with stronger, i.e., more positive sponsor-related network externalities. It follows that the equilibrium demands q\ and qÇ are higher in a situation in which the combined network effects are positive than in a situation in which the combined network effects are zero. Ceteris paribus, an increase in ns (i.e., either weaker negative or stronger positive sponsor-related network externalities) yields increased combined network effects and thus leads to an increase in the demand of fans. In combination with the positive fan-related network externalities, this induces an increase in demand on the part of sponsors. Part (ii) of the lemma is also in line with the literature on two-sided markets and shows that given a certain quality of the competition the equilibrium price for the fans of club i is lower and the equilibrium price p\ for the sponsors is higher, the stronger are the positive fan-related network externalities nf. Relatively stronger fan-related network externalities induce an increase in the demand function of the sponsors and yield, ceteris paribus, an increase in the prices for sponsors. The opposite holds true for weaker negative or stronger positive sponsor-related network externalities. Hence, if club i decreases the price for the market with the stronger positive network externalities (in our model the fan market), it enhances the positive effect on revenues (Armstrong 2006). It follows that due to the positive network externalities exerted by the fans on the sponsors, a revenue-maximizing club has an incentive to keep prices low on the market with the positive network externalities (fan market), whereas in the market with relatively weaker positive or even negative network externalities (sponsor market), it has an incentive to charge higher prices. We derive that equilibrium prices for fans (sponsors) are lower (higher) in a situation with positive combined network effects than in a situation in which combined network effects equal zero. By substituting equilibrium prices and quantities of fans and sponsors from (8) and (9) in the revenue function (6), we compute the revenue of club i as 1 8 R,- = K,--fl,- = ^

( x ,

' + 2g·), (.X¡ + Xj)

(10)

with _ {m{f

+ (ms)2+wfwsy

(2 — η) (2 + η)

'

( Π )

In the next lemma, we derive some useful properties of the sponsor- and fan-related revenue function K¡, which will be exploited in the subsequent analysis.

18

The revenue function given by (10) satisfies the properties of the revenue function proposed by Szymanski and Késenne (2004: 168).

346 · Helmut Dietl, Tobias Duschl, Egon Franck, and Markus Lang

Lemma 3 We consider κ ¡(η) as a function of the combined network externalities following properties: κ ι {η) > κι{η) and δκι(η)/ δη > όι 0. Proof. Straightforward and therefore omitted.

η and derive the

It follows from Lemma 3 that given a certain quality of competition equal for both clubs (i.e., θ\ = θχ), the sponsor- and fan-related revenue of the large club will be higher than the revenue of the small club. Moreover, sponsor- and fan-related revenues for both types of clubs increase with stronger combined network effects, where the increase is stronger for the large club than for the small club. 4.2 Stage 1 In stage 1, club i maximizes its profits by anticipating the decisions made in stage 2. By substituting club revenues (10) into the profit function (7), we derive the maximization problem of club i in stage 1 as r ι ({m^)2+ max π, = R¡(x¡,xj) - ex, f = —'—

{ms)2+mfim^\xi{x, '

+ 2xj) - f - - ex,.

(12)

The first-order conditions for this maximization problem yield19 άπί_

Í{mfj)2 + (2-η)(2

2xj + η)

_

c

— Q

)(χ,+χΐ)3

Solving this system of equations, yields the equilibrium talent investments of club i in stage 1 as

=

2k,Ki\K,(K¡ + 3κ,) - (K,7C,)1/2(3K, + κ,·) L i· ; ^ C(K, - Kj)

(13)

Both types of clubs invest a positive amount x¡ > 0 in playing talent. Moreover, the large club invests more in talent than the small club (i.e., x\ > χι) because the marginal revenue of talent investments is higher for the former type of club due to the larger market potential of its fans. 20 Note that the investments of both clubs are influenced by the network externalities exerted by fans and sponsors. Again, the extent to which fans and sponsors indirectly influence each other determines the decision of each club to invest in playing talent. Substituting the equilibrium investments (13) into the CSF (3) yields the following equilibrium win percentages: (¿>1>2)= ( \Kl + (K1K2) '

iti)· K2 + (K1K2) ' /

(14)

By analyzing the impact of network externalities on the win percentages, we can establish the following proposition. 19 20

It is easy to verify that the second-order conditions for a m a x i m u m are satisfied. See Buraimo et al. ( 2 0 0 7 ) , w h o analyze h o w playing success is linked to market size in practice.

A Contest M o d e l of a Professional Sports League with Two-Sided Markets · 347

Proposition 1 Stronger combined network effects η induce the large (small) club to decrease league (increase) its win percentage in equilibrium and thus produce a more balanced if and only if the market potential of the sponsors is sufficiently small. Formally, ΰίν\/άη < 0 and dw2/ty > 0 ms < ms = (m[mf2)1/2. Proof. See Appendix A3. The proposition shows that with a sufficiently small market potential of the sponsors, i.e., ms < ms, the win percentage of the large (small) club decreases (increases) with stronger positive fan-related network externalities. Weaker negative or stronger positive sponsor-related network externalities yield the same result. The intuition behind this result is as follows. Stronger combined network effects have a positive impact on marginal revenue of both clubs such that both clubs will increase their investment levels. To determine which club increases its investments more strongly, we have to analyze the relationship between fans' market sizes and the sponsor's market potential. The difference in market sizes for the two clubs regarding their fan base yields that sponsor-related revenues are relatively more important to the small club than to the large club. It follows that the marginal impact on club revenues of stronger combined network effects is greater for the small club than for the large club. As a result, the small club increases its investment in talent stronger than the large club as combined network effects increase. For the large club, the opposite rationale holds. In equilibrium, the large club increases its investment level less strongly than the small club, thereby decreasing its win percentage. Consequently, with stronger combined network externalities competitive balance increases. Thus, a league in which the positive fan-related network externalities are stronger than the sponsor-related network externalities (in absolute value) may be characterized by a higher degree of competitive balance than a league in which combined network effects are zero. For a sufficiently large market potential of the sponsors, i. e., ms > ms, the opposite holds true. In this case, competitive balance decreases if combined network effects increase. Furthermore, note that the quality of the competition 0¡ in equilibrium can be expressed in terms of κ, as 2

~

~ ~

0; = W¡ + WjWj

Ki(2Kj + (K,7C,)1/2)

= • ' (Ki + (KiKi)1f2)(Ki

' +

(KiKi)l/2y

We derive that stronger combined network effects imply a lower (higher) quality of competition for the large (small) club if and only if the market potential of the sponsors is sufficiently small. Formally, (άθ\/όη < 0 and ΰθιβη > 0) ms